Related papers: Relative modular classes of Lie algebroids
The notion of crossed modules for Lie 2-algebras is introduced. We show that, associated to such a crossed module, there is a strict Lie 3-algebra structure on its mapping cone complex and a strict Lie 2-algebra structure on its…
We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case…
We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and…
We show that every Lie algebroid $A$ over a manifold $P$ has a natural representation on the line bundle $Q_A = \wedge^{top}A \otimes \wedge^{top} T^*P$. The line bundle $Q_A$ may be viewed as the Lie algebroid analog of the orientation…
A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity…
We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.
Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of…
We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct quasi-Lie bialgebroids from quasi-Jacobi bialgebroids, and conversely, and also that…
In this paper we investigate classifications of all (transposed) Poisson algebras of the associated associative null-filiform algebra
The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also…
We describe (braided-)commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over…
We consider a class of infinite-dimensional, modular, graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. We identify two subclasses of Nottingham Lie…
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint…
We explicitly construct families of simple modules for Lie algebras of rank $2$, on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ these modules are well known generic Gelfand-Tsetlin modules and…
Some cohomology classes associated with an ideal in a Lie algebra, a Poisson structure on the basic functions algebra of contact structure, its Poisson cohomology and geometric (pre)quantization are considered from the algebraic point of…
We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…
We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a…